Tides
for the hypothetical case of an ocean of constant depth without land. There would also be smaller, superimposed bulges on the sides facing toward and away from the Sun.}} (U.S.), low tide occurs roughly at moonrise and high tide with a high Moon, corresponding to the simple gravity model of two tidal bulges; at most places however, the Moon and tides have a .}} Tides are the rise and fall of s caused by the combined effects of the forces exerted by the and the , and the of the . s can be used for any given locale to find the predicted times and amplitude (or " "). The predictions are influenced by many factors including the alignment of the Sun and Moon, the (pattern of tides in the deep ocean), the systems of the oceans, and the shape of the coastline and near-shore (see ). They are however only predictions, the actual time and height of the tide is affected by wind and atmospheric pressure. Many shorelines experience tides—two nearly equal high and low tides each day. Other locations have a tide—one high and low tide each day. A "mixed tide"—two uneven magnitude tides a day—is a third regular category. Tides vary on timescales ranging from hours to years due to a number of factors, which determine the . To make accurate records, s at fixed stations measure water level over time. Gauges ignore variations caused by waves with periods shorter than minutes. These data are compared to the reference (or datum) level usually called . While tides are usually the largest source of short-term sea-level fluctuations, sea levels are also subject to forces such as wind and barometric pressure changes, resulting in s, especially in shallow seas and near coasts. Tidal phenomena are not limited to the oceans, but can occur in other systems whenever a gravitational field that varies in time and space is present. For example, the shape of the solid part of the Earth is affected slightly by , though this is not as easily seen as the water tidal movements. Characteristics Tide changes proceed via the following stages: * Sea level rises over several hours, covering the ; flood tide. * The water rises to its highest level, reaching high tide. * Sea level falls over several hours, revealing the intertidal zone; ebb tide. * The water stops falling, reaching low tide. Oscillating currents produced by tides are known as tidal streams. The moment that the tidal current ceases is called or slack tide. The tide then reverses direction and is said to be turning. Slack water usually occurs near high water and low water. But there are locations where the moments of slack tide differ significantly from those of high and low water. Tides are commonly semi-diurnal (two high waters and two low waters each day), or diurnal (one tidal cycle per day). The two high waters on a given day are typically not the same height (the daily inequality); these are the higher high water and the lower high water in s. Similarly, the two low waters each day are the higher low water and the lower low water. The daily inequality is not consistent and is generally small when the Moon is over the . Definitions From the highest level to the lowest: * Highest astronomical tide (HAT) – The highest tide which can be predicted to occur. Note that meteorological conditions may add extra height to the HAT. * Mean high water springs (MHWS) – The average of the two high tides on the days of spring tides. * Mean high water neaps (MHWN) – The average of the two high tides on the days of neap tides. * Mean sea level (MSL) – This is the average sea level. The MSL is constant for any location over a long period. * Mean low water neaps (MLWN) – The average of the two low tides on the days of neap tides. * Mean low water springs (MLWS) – The average of the two low tides on the days of spring tides. * Lowest astronomical tide (LAT) and Chart Datum (CD) – The lowest tide which can be predicted to occur. Modern charts use this as the chart datum. Note that under certain meteorological conditions the water may fall lower than this meaning that there is less water than shown on charts. Tidal constituents Tidal constituents are the net result of multiple influences impacting tidal changes over certain periods of time. Primary constituents include the Earth's rotation, the position of the Moon and Sun relative to the Earth, the Moon's altitude (elevation) above the Earth's Equator, and . Variations with periods of less than half a day are called harmonic constituents. Conversely, cycles of days, months, or years are referred to as long period constituents. Tidal forces , but the movement of solid Earth occurs by mere centimeters. In contrast, the atmosphere is much more fluid and compressible so its surface moves by kilometers, in the sense of the contour level of a particular low pressure in the outer atmosphere. Principal lunar semi-diurnal constituent In most locations, the largest constituent is the "principal lunar semi-diurnal", also known as the M2 (or M''2) tidal constituent. Its period is about 12 hours and 25.2 minutes, exactly half a ''tidal lunar day, which is the average time separating one lunar from the next, and thus is the time required for the Earth to rotate once relative to the Moon. Simple s track this constituent. The lunar day is longer than the Earth day because the Moon orbits in the same direction the Earth spins. This is analogous to the minute hand on a watch crossing the hour hand at 12:00 and then again at about 1:05½ (not at 1:00). The Moon orbits the Earth in the same direction as the Earth rotates on its axis, so it takes slightly more than a day—about 24 hours and 50 minutes—for the Moon to return to the same location in the sky. During this time, it has passed overhead ( ) once and underfoot once (at an of 00:00 and 12:00 respectively), so in many places the period of strongest tidal forcing is the above-mentioned, about 12 hours and 25 minutes. The moment of highest tide is not necessarily when the Moon is nearest to or , but the period of the forcing still determines the time between high tides. Because the gravitational field created by the Moon weakens with distance from the Moon, it exerts a slightly stronger than average force on the side of the Earth facing the Moon, and a slightly weaker force on the opposite side. The Moon thus tends to "stretch" the Earth slightly along the line connecting the two bodies. The solid Earth deforms a bit, but ocean water, being fluid, is free to move much more in response to the tidal force, particularly horizontally. As the Earth rotates, the magnitude and direction of the tidal force at any particular point on the Earth's surface change constantly; although the ocean never reaches equilibrium—there is never time for the fluid to "catch up" to the state it would eventually reach if the tidal force were constant—the changing tidal force nonetheless causes rhythmic changes in sea surface height. When there are two high tides each day with different heights (and two low tides also of different heights), the pattern is called a mixed semi-diurnal tide. Range variation: springs and neaps The semi-diurnal range (the difference in height between high and low waters over about half a day) varies in a two-week cycle. Approximately twice a month, around and when the Sun, Moon, and Earth form a line (a configuration known as a ), the due to the Sun reinforces that due to the Moon. The tide's range is then at its maximum; this is called the spring tide. It is not named after the , but, like that word, derives from the meaning "jump, burst forth, rise", as in a natural . When the Moon is at or third quarter, the Sun and Moon are separated by 90° when viewed from the Earth, and the solar tidal force partially cancels the Moon's tidal force. At these points in the lunar cycle, the tide's range is at its minimum; this is called the neap tide, or neaps. Neap is an Anglo-Saxon word meaning "without the power", as in forðganges nip (forth-going without-the-power). Spring tides result in high waters that are higher than average, low waters that are lower than average, ' ' time that is shorter than average, and stronger tidal currents than average. Neaps result in less extreme tidal conditions. There is about a seven-day interval between springs and neaps. File:High tide sun moon same side beginning.png|'Spring tide:' Sun and Moon on the same side (0°) File:Low tide sun moon 90 degrees.png|'Neap tide:' Sun and Moon at 90° File:High tide sun moon opposite side.png|'Spring tide:' Sun and Moon at opposite sides (180°) File:Low tide sun moon 270 degrees.png|'Neap tide:' Sun and Moon at 270° File:High tide sun moon same side end.png|'Spring tide:' Sun and Moon at the same side (cycle restarts) Lunar altitude , , }} in , , U.S.}} , , U.S. (2014)}} The changing distance separating the Moon and Earth also affects tide heights. When the Moon is closest, at , the range increases, and when it is at , the range shrinks. Every s (the full cycles from full moon to new to full), perigee coincides with either a new or full moon causing s with the largest . Even at its most powerful this force is still weak, causing tidal differences of inches at most. Other constituents These include solar gravitational effects, the obliquity (tilt) of the Earth's Equator and rotational axis, the inclination of the plane of the lunar orbit and the elliptical shape of the Earth's orbit of the Sun. A compound tide (or overtide) results from the shallow-water interaction of its two parent waves. Phase and amplitude s. The curved arcs around the amphidromic points show the direction of the tides, each indicating a synchronized 6-hour period. Tidal ranges generally increase with increasing distance from amphidromic points. Tide waves move around these points, generally counterclockwise in the N. Hemisphere and clockwise in the S. Hemisphere |alt=Map showing relative tidal magnitudes of different ocean areas}} Because the ''M''2 tidal constituent dominates in most locations, the stage or ''phase of a tide, denoted by the time in hours after high water, is a useful concept. Tidal stage is also measured in degrees, with 360° per tidal cycle. Lines of constant tidal phase are called cotidal lines, which are analogous to of constant altitude on , and when plotted form a cotidal map or cotidal chart. High water is reached simultaneously along the cotidal lines extending from the coast out into the ocean, and cotidal lines (and hence tidal phases) advance along the coast. Semi-diurnal and long phase constituents are measured from high water, diurnal from maximum flood tide. This and the discussion that follows is precisely true only for a single tidal constituent. For an ocean in the shape of a circular basin enclosed by a coastline, the cotidal lines point radially inward and must eventually meet at a common point, the . The amphidromic point is at once cotidal with high and low waters, which is satisfied by zero tidal motion. (The rare exception occurs when the tide encircles an island, as it does around New Zealand, and .) Tidal motion generally lessens moving away from continental coasts, so that crossing the cotidal lines are contours of constant amplitude (half the distance between high and low water) which decrease to zero at the amphidromic point. For a semi-diurnal tide the amphidromic point can be thought of roughly like the center of a clock face, with the hour hand pointing in the direction of the high water cotidal line, which is directly opposite the low water cotidal line. High water rotates about the amphidromic point once every 12 hours in the direction of rising cotidal lines, and away from ebbing cotidal lines. This rotation, caused by the , is generally clockwise in the southern hemisphere and counterclockwise in the northern hemisphere. The difference of cotidal phase from the phase of a reference tide is the epoch. The reference tide is the hypothetical constituent "equilibrium tide" on a landless Earth measured at 0° longitude, the Greenwich meridian. In the North Atlantic, because the cotidal lines circulate counterclockwise around the amphidromic point, the high tide passes New York Harbor approximately an hour ahead of Norfolk Harbor. South of Cape Hatteras the tidal forces are more complex, and cannot be predicted reliably based on the North Atlantic cotidal lines. Physics History of tidal physics Investigation into tidal physics was important in the early development of , with the existence of two daily tides being explained by the Moon's gravity. Later the daily tides were explained more precisely by the interaction of the Moon's and the Sun's gravity. theorized around 150 BC that tides were caused by the Moon. The influence of the Moon on bodies of water was also mentioned in 's . In De temporum ratione ( ) of 725 linked semidurnal tides and the phenomenon of varying tidal heights to the Moon and its phases. Bede starts by noting that the tides rise and fall 4/5 of an hour later each day, just as the Moon rises and sets 4/5 of an hour later. He goes on to emphasise that in two lunar months (59 days) the Moon circles the Earth 57 times and there are 114 tides. Bede then observes that the height of a tides varies over the month. Increasing tides are called malinae and decreasing tides ledones and that the month is divided into four parts of seven or eight days with alternating malinae and ledones. In the same passage he also notes the effect of winds to hold back tides. Bede also records that the time of tides varies from place to place. To the north of Bede's location ( ) the tides are earlier, to the south later. He explains that the tide "deserts these shores in order to be able all the more to be able to flood other shores when it arrives there" noting that "the Moon which signals the rise of tide here, signals its retreat in other regions far from this quarter of the heavens". Medieval understanding of the tides was primarily based on works of , which became available through starting from the 12th century. (d. circa 886), in his Introductorium in astronomiam, taught that ebb and flood tides were caused by the Moon. Abu Ma'shar discussed the effects of wind and Moon's phases relative to the Sun on the tides. In the 12th century, (d. circa 1204) contributed the notion that the tides were caused by the general circulation of the heavens. in his 1608 De spiegheling der Ebbenvloet, The theory of ebb and flood, dismissed a large number of misconceptions that still existed about ebb and flood. Stevin pleaded for the idea that the attraction of the Moon was responsible for the tides and spoke in clear terms about ebb, flood, and , stressing that further research needed to be made. In 1609 also correctly suggested that the gravitation of the Moon caused the tides, which he based upon ancient observations and correlations. in his 1632 , whose working title was Dialogue on the Tides, gave an explanation of the tides. The resulting theory, however, was incorrect as he attributed the tides to the sloshing of water caused by the Earth's movement around the Sun. He hoped to provide mechanical proof of the Earth's movement. The value of his tidal theory is disputed. Galileo rejected Kepler's explanation of the tides. (1642–1727) was the first person to explain tides as the product of the gravitational attraction of astronomical masses. His explanation of the tides (and many other phenomena) was published in the (1687) and used his to explain the lunar and solar attractions as the origin of the tide-generating forces. Newton and others before worked the problem from the perspective of a static system (equilibrium theory), that provided an approximation that described the tides that would occur in a non-inertial ocean evenly covering the whole Earth. The tide-generating force (or its corresponding ) is still relevant to tidal theory, but as an intermediate quantity (forcing function) rather than as a final result; theory must also consider the Earth's accumulated dynamic tidal response to the applied forces, which response is influenced by ocean depth, the Earth's rotation, and other factors. In 1740, the in Paris offered a prize for the best theoretical essay on tides. , , and shared the prize. Maclaurin used Newton's theory to show that a smooth sphere covered by a sufficiently deep ocean under the tidal force of a single deforming body is a spheroid (essentially a three-dimensional oval) with major axis directed toward the deforming body. Maclaurin was the first to write about the Earth's on motion. Euler realized that the tidal force's horizontal component (more than the vertical) drives the tide. In 1744 studied tidal equations for the atmosphere which did not include rotation. In 1770 's grounded on the . Attempts were made to refloat her on the following tide which failed, but the tide after that lifted her clear with ease. Whilst she was being repaired in the mouth of the Cook observed the tides over a period of seven weeks. At neap tides both tides in a day were similar, but at springs the tides rose in the morning but in the evening. Pierre-Simon Laplace formulated a system of s relating the ocean's horizontal flow to its surface height, the first major dynamic theory for water tides. The are still in use today. , rewrote Laplace's equations in terms of which allowed for solutions describing tidally driven coastally trapped waves, known as s. Others including Kelvin and further developed Laplace's theory. Based on these developments and the of describing the motions of the Moon, developed and published in 1921 the first modern development of the tide-generating potential in harmonic form: Doodson distinguished 388 tidal frequencies. Some of his methods remain in use. Forces The produced by a massive object (Moon, hereafter) on a small particle located on or in an extensive body (Earth, hereafter) is the vector difference between the gravitational force exerted by the Moon on the particle, and the gravitational force that would be exerted on the particle if it were located at the Earth's center of mass. Whereas the subjected by a celestial body on Earth varies inversely as the square of its distance to the Earth, the maximal tidal force varies inversely as, approximately, the cube of this distance. If the tidal force caused by each body were instead equal to its full gravitational force (which is not the case due to the of the whole Earth, not only the oceans, towards these bodies) a different pattern of tidal forces would be observed, e.g. with a much stronger influence from the Sun than from the Moon: The solar gravitational force on the Earth is on average 179 times stronger than the lunar, but because the Sun is on average 389 times farther from the Earth, its field gradient is weaker. The solar tidal force is 46% as large as the lunar. More precisely, the lunar tidal acceleration (along the Moon–Earth axis, at the Earth's surface) is about 1.1 × 10−7 g'', while the solar tidal acceleration (along the Sun–Earth axis, at the Earth's surface) is about 0.52 × 10−7 ''g, where g'' is the at the Earth's surface. Venus has the largest effect of the other planets, at 0.000113 times the solar effect. The system of the Earth, the Moon and the Sun is an example of a , and there is no exact mathematical of their interdependence. differential at the Earth's surface is known as the . This is the primary mechanism that drives tidal action and explains two equipotential tidal bulges, accounting for two daily high waters.|alt=Diagram showing a circle with closely spaced arrows pointing away from the reader on the left and right sides, while pointing towards the user on the top and bottom.}} The ocean's surface is closely approximated by an equipotential surface, (ignoring ocean currents) commonly referred to as the . Since the gravitational force is equal to the potential's , there are no ial forces on such a surface, and the ocean surface is thus in gravitational equilibrium. Now consider the effect of massive external bodies such as the Moon and Sun. These bodies have strong gravitational fields that diminish with distance and act to alter the shape of an equipotential surface on the Earth. This deformation has a fixed spatial orientation relative to the influencing body. The Earth's rotation relative to this shape causes the daily tidal cycle. The ocean surface moves because of the changing tidal equipotential, rising when the tidal potential is high, which occurs on the parts of the Earth nearest to and furthest from the Moon. When the tidal equipotential changes, the ocean surface is no longer aligned with it, so the apparent direction of the vertical shifts. The surface then experiences a down slope, in the direction that the equipotential has risen. Laplace's tidal equations Ocean depths are much smaller than their horizontal extent. Thus, the response to tidal forcing can be using the which incorporate the following features: # The vertical (or radial) velocity is negligible, and there is no vertical —this is a sheet flow. # The forcing is only horizontal ( ial). # The appears as an inertial force (fictitious) acting laterally to the direction of flow and proportional to velocity. # The surface height's rate of change is proportional to the negative divergence of velocity multiplied by the depth. As the horizontal velocity stretches or compresses the ocean as a sheet, the volume thins or thickens, respectively. The boundary conditions dictate no flow across the coastline and free slip at the bottom. The Coriolis effect (inertial force) steers flows moving towards the Equator to the west and flows moving away from the Equator toward the east, allowing coastally trapped waves. Finally, a dissipation term can be added which is an analog to viscosity. Amplitude and cycle time The theoretical amplitude of oceanic tides caused by the Moon is about at the highest point, which corresponds to the amplitude that would be reached if the ocean possessed a uniform depth, there were no landmasses, and the Earth were rotating in step with the Moon's orbit. The Sun similarly causes tides, of which the theoretical amplitude is about (46% of that of the Moon) with a cycle time of 12 hours. At spring tide the two effects add to each other to a theoretical level of , while at neap tide the theoretical level is reduced to . Since the orbits of the Earth about the Sun, and the Moon about the Earth, are elliptical, tidal amplitudes change somewhat as a result of the varying Earth–Sun and Earth–Moon distances. This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun. If both the Sun and Moon were at their closest positions and aligned at new moon, the theoretical amplitude would reach . Real amplitudes differ considerably, not only because of depth variations and continental obstacles, but also because wave propagation across the ocean has a natural period of the same order of magnitude as the rotation period: if there were no land masses, it would take about 30 hours for a long wavelength surface wave to propagate along the Equator halfway around the Earth (by comparison, the Earth's has a natural period of about 57 minutes). s, which raise and lower the bottom of the ocean, and the tide's own gravitational self attraction are both significant and further complicate the ocean's response to tidal forces. Dissipation Earth's tidal oscillations introduce dissipation at an rate of about 3.75 s. About 98% of this dissipation is by marine tidal movement. Dissipation arises as basin-scale tidal flows drive smaller-scale flows which experience turbulent dissipation. This tidal drag creates torque on the moon that gradually transfers angular momentum to its orbit, and a gradual increase in Earth–moon separation. The equal and opposite torque on the Earth correspondingly decreases its rotational velocity. Thus, over geologic time, the moon recedes from the Earth, at about /year, lengthening the terrestrial day. by about 2 hours in the last 600 million years. Assuming (as a crude approximation) that the deceleration rate has been constant, this would imply that 70 million years ago, day length was on the order of 1% shorter with about 4 more days per year. Bathymetry falls dry at low tide.}} The shape of the shoreline and the ocean floor changes the way that tides propagate, so there is no simple, general rule that predicts the time of high water from the Moon's position in the sky. Coastal characteristics such as underwater and coastline shape mean that individual location characteristics affect tide forecasting; actual high water time and height may differ from model predictions due to the coastal morphology's effects on tidal flow. However, for a given location the relationship between lunar and the time of high or low tide (the ) is relatively constant and predictable, as is the time of high or low tide relative to other points on the same coast. For example, the high tide at , U.S., predictably occurs approximately two and a half hours before the Moon passes directly overhead. Land masses and ocean basins act as barriers against water moving freely around the globe, and their varied shapes and sizes affect the size of tidal frequencies. As a result, tidal patterns vary. For example, in the U.S., the East coast has predominantly semi-diurnal tides, as do Europe's Atlantic coasts, while the West coast predominantly has mixed tides. Biological aspects Intertidal ecology Intertidal ecology is the study of s between the low- and high-water lines along a shore. At low water, the intertidal zone is exposed (or ''emersed), whereas at high water, it is underwater (or immersed). Intertidal s therefore study the interactions between intertidal organisms and their environment, as well as among the . The most important interactions may vary according to the type of intertidal community. The broadest classifications are based on substrates — or soft bottom. Intertidal organisms experience a highly variable and often hostile environment, and have to cope with and even exploit these conditions. One easily visible feature is , in which the community divides into distinct horizontal bands of specific species at each elevation above low water. A species' ability to cope with determines its upper limit, while with other species sets its lower limit. Humans for food and recreation. can damage intertidals directly. Other anthropogenic actions such as introducing and have large negative effects. s are one option communities can apply to protect these areas and aid scientific . Biological rhythms The approximately fortnightly tidal cycle has large effects on intertidal and marine organisms. Hence their s tend to occur in rough multiples of this period. Many other animals such as the s, display similar rhythms. Examples include and egg hatching. In humans, the lasts roughly a , an even multiple of the tidal period. Such parallels at least hint at the of all animals from a marine ancestor. Other tides When oscillating tidal currents in the stratified ocean flow over uneven bottom topography, they generate s with tidal frequencies. Such waves are called s. Shallow areas in otherwise open water can experience rotary tidal currents, flowing in directions that continually change and thus the flow direction (not the flow) completes a full rotation in hours (for example, the ). In addition to oceanic tides, large lakes can experience small tides and even planets can experience s and s. These are phenomena. The first two take place in s. The third affects the Earth's thin crust surrounding its semi-liquid interior (with various modifications). Lake tides Large lakes such as and can experience tides of 1 to 4 cm (0.39 to 1.6 in), but these can be masked by meteorologically induced phenomena such as . The tide in is described as 0.5 to 1.5 inches (13 to 38 mm) or 1 inches. This is so small that other larger effects completely mask any tide, and as such these lakes are considered non-tidal. Atmospheric tides Atmospheric tides are negligible at ground level and aviation altitudes, masked by 's much more important effects. Atmospheric tides are both gravitational and thermal in origin and are the dominant dynamics from about 80 to 120 kilometres (50 to 75 mi), above which the molecular density becomes too low to support fluid behavior. Earth tides Earth tides or terrestrial tides affect the entire Earth's mass, which acts similarly to a liquid with a very thin crust. The Earth's crust shifts (in/out, east/west, north/south) in response to lunar and solar gravitation, ocean tides, and atmospheric loading. While negligible for most human activities, terrestrial tides' semi-diurnal amplitude can reach about at the Equator— due to the Sun—which is important in calibration and measurements. Precise astronomical angular measurements require knowledge of the Earth's rotation rate and , both of which are influenced by Earth tides. The semi-diurnal M''2 Earth tides are nearly in phase with the Moon with a lag of about two hours. Galactic tides '' s are the tidal forces exerted by galaxies on stars within them and orbiting them. The galactic tide's effects on the 's are believed to cause 90 percent of long-period comets. References Category:Intermediate Physics